A Meshless Symplectic Algorithm for multi-variate Hamiltonian PDEs with Radial Basis Approximation. (January 2015)

• Record Type: Journal Article
• Authors: Wu, Z.; Zhang, S.
• Is Part Of: Engineering analysis with boundary elements. Volume 50(2015:Jan.)
• Page Start: 258
• Page End: 264
• Publication Date: 2015-01
• Subjects: Meshless method -- Radial basis interpolation -- Energy conservation -- Hamiltonian system -- Symplectic integrator; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2014.08.015
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: Based on radial basis approximation, in this paper we propose two methods to discretize the problem of multi-variate Hamiltonian system. One is discretizing the system and finding out the corresponding discrete Hamiltonian functional, which will be conserved with respect to the time. The other is discretizing the Hamiltonian functional and deriving the corresponding discrete Hamiltonian system. This helps open a new area of research in developing the expected meshless symplectic algorithm for multi-variate Hamiltonian systems with the scattered data points. Theoretical estimates including the truncation error and the global error are given. Numerical experiments verify the theoretical results. As numerical experiments show, the schemes are easy to implement with the scattered knots. Furthermore, the schemes possesss a long-time tracking capability for these Hamiltonian systems.